The multiple holomorph of a finitely generated abelian group

DOI10.1016/j.jalgebra.2017.03.006zbMath1448.20004arXiv1611.05662OpenAlexW2554839519MaRDI QIDQ527785

Andrea Caranti, Francesca Dalla Volta

Publication date: 12 May 2017

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05662

zbMATH Keywords

commutative ringsholomorphfinitely-generated abelian groupsmultiple holomorph

Mathematics Subject Classification ID

Automorphisms of abstract finite groups (20D45) Automorphisms of infinite groups (20E36) Extensions, wreath products, and other compositions of groups (20E22) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Subgroups of symmetric groups (20B35)

Related Items

On the holomorph of finite semisimple groups, Groups that have the same holomorph as a finite perfect group, Mutually normalizing regular permutation groups and Zappa-Szép extensions of the holomorph, The multiple holomorph of split metacyclic p-groups, Hopf-Galois structures on extensions of degree \(p^2q\) and skew braces of order \(p^2q\): the cyclic Sylow \(p\)-subgroup case, The multiple holomorph of a semidirect product of groups having coprime exponents, Module braces: relations between the additive and the multiplicative groups, Finite \(p\)-groups of class two with a small multiple holomorph, Bi-skew braces and regular subgroups of the holomorph, Multiple holomorphs of finite \(p\)-groups of class two, On the multiple holomorph of groups of squarefree or odd prime power order, Finite \(p\)-groups of class two with a large multiple holomorph

Cites Work

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• Abelian Hopf Galois structures on prime-power Galois field extensions
• Multiple Holomorphs of Dihedral and Quaternionic Groups
• Multiple Holomorphs of Finitely Generated Abelian Groups
• On the Non-Isomorphism of Certain Holomorphs